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Results in Mathematics

, Volume 32, Issue 1–2, pp 145–158 | Cite as

Stability of the Cauchy type equations in \( {\cal L}_p \) norms

  • Józef Tabor
Article

Abstract

Let (X, +, μ) be a measurable group such that μ is complete and μ(X) = ∞, and let (E, +) be a metric group. Let f: X → E be any mapping. We prove that if there exists a p > 0 such that the function \((d(f(x + y), f(x) + f(y)))^p \) is majorizable by an integrable function then f is almost everywhere additive. Similar results we also obtain for the Jensen and Pexider equations.

1991 Mathematics Subject Classification

39B72 

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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  1. 1.Pedagogical University in RzeszöwRzeszowPoland

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